Problem: Luis is 4 times as old as Vanessa. Ten years ago, Luis was 9 times as old as Vanessa. How old is Luis now?
Explanation: We can use the given information to write down two equations that describe the ages of Luis and Vanessa. Let Luis's current age be $l$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $l = 4v$ Ten years ago, Luis was $l - 10$ years old, and Vanessa was $v - 10$ years old. The information in the second sentence can be expressed in the following equation: $l - 10 = 9(v - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = l / 4$ . Substituting this into our second equation, we get: $l - 10 = 9($ $(l / 4)$ $- 10)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $l - 10 = \dfrac{9}{4} l - 90$ Solving for $l$ , we get: $\dfrac{5}{4} l = 80$ $l = \dfrac{4}{5} \cdot 80 = 64$.